The study tracked behavior in 1,037 mostly disadvantaged Quebec schoolboys from kindergarten through age 18. The boys fell into four distinct trajectories of physical aggression.

The most peaceable 20 percent, a “no problem” group, showed little physical aggression at any age; two larger groups showed moderate and high rates of aggression as preschoolers. In these three groups violence fell through childhood and adolescence, and dropped to almost nothing when the boys reached their 20s.

A fourth group, about 5 percent, peaked higher during toddlerhood and declined far more slowly. Their curve was more plateau than hill.

As they moved into late adolescence and young adulthood, their aggression grew ever more dangerous, and it tailed off late. At age 17 they were four times as physically aggressive as the moderate group and committed 14 times as many criminal infractions. It’s these chronically violent individuals, Dr. Tremblay says, who are responsible for most violent crime.